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Mathematical Delights is a collection of 90 short elementary gems from algebra, geometry, combinatorics, and number theory. Ross Honsberger presents us with some surprising results, brilliant ideas, and beautiful arguments in mathematics, written in his wonderfully lucid style. The book is a mathematical entertainment to be read at a leisurely pace. High school mathematics should equip the reader to handle the problems presented in the book. The topics are entirely independent and can be read in any order. A useful set of indices helps the reader locate topics in the text.
Trigonometry has always been an underappreciated branch of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a compelling blend of history, biography, and mathematics. He presents both a survey of the main elements of trigonometry and a unique account of its vital contribution to science and social development. Woven together in a tapestry of entertaining stories, scientific curiosities, and educational insights, the book more than lives up to the title Trigonometric Delights. ? Maor, whose previous books have demystified the concept of infinity and the unusual number "e," begins by examining the "proto-trigonometry" of the Egyptian pyramid builders. He shows how Greek astronomers developed the first true trigonometry. He traces the slow emergence of modern, analytical trigonometry, recounting its colorful origins in Renaissance Europe's quest for more accurate artillery, more precise clocks, and more pleasing musical instruments. Along the way, we see trigonometry at work in, for example, the struggle of the famous mapmaker Gerardus Mercator to represent the curved earth on a flat sheet of paper; we see how M. C. Escher used geometric progressions in his art; and we learn how the toy Spirograph uses epicycles and hypocycles. Maor also sketches the lives of some of the intriguing figures who have shaped four thousand years of trigonometric history. We meet, for instance, the Renaissance scholar Regiomontanus, who is rumored to have been poisoned for insulting a colleague, and Maria Agnesi, an eighteenth-century Italian genius who gave up mathematics to work with the poor--but not before she investigated a special curve that, due to mistranslation, bears the unfortunate name "the witch of Agnesi." The book is richly illustrated, including rare prints from the author's own collection. Trigonometric Delights will change forever our view of a once dreaded subject.
'The main object of this book is to dispel the fear of mathematics. Many people regard mathematicians as a race apart, possessed of almost supernatural powers. While this is very flattering for successful mathematicians, it is very bad for those who, for one reason or another, are attempting to learn the subject.' W.W. Sawyer's deep understanding of how we learn and his lively, practical approach have made this an ideal introduction to mathematics for generations of readers. By starting at the level of simple arithmetic and algebra and then proceeding step by step through graphs, logarithms and trigonometry to calculus and the dizzying world of imaginary numbers, the book takes the mystery out of maths. Throughout, Sawyer reveals how theory is subordinate to the real-life applications of mathematics - the Pyramids were built on Euclidean principles three thousand years before Euclid formulated them - and celebrates the sheer intellectual stimulus of mathematics at its best.
Portal through Mathematics: Journey to Advanced Thinking by O. A. Ivanov Pdf
Portal through Mathematics is a collection of puzzles and problems mostly on topics relating to secondary mathematics. The problems and topics are fresh and interesting and frequently surprising. One example: the puzzle that asks how much length must be added to a belt around the Earth's equator to raise it one foot has probably achieved old chestnut status. Ivanov, after explaining the surprising answer to this question, goes a step further and asks, if you grabbed that too long belt at some point and raised it as high as possible, how high would that be? The answer to that is more surprising than the classic puzzle's answer. The book is organized into 29 themes, each a topic from algebra, geometry or calculus and each launched from an opening puzzle or problem. There are excursions into number theory, solid geometry, physics and combinatorics. Always there is an emphasis on surprise and delight. And every theme begins at a level approachable with minimal background requirements. With well over 250 puzzles and problems, there is something here sure to appeal to everyone. Portal through Mathematics will be useful for prospective secondary teachers of mathematics and may be used (as a supplementary resource) in university courses in algebra, geometry, calculus, and discrete mathematics. It can also be used for professional development for teachers looking for inspiration. However, the intended audience is much broader. Every fan of mathematics will find enjoyment in it.
The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan Pdf
“A great storyteller.”—Paulo Coelho, author of The Alchemist Malba Tahan is the creation of a celebrated Brazilian mathematician looking for a way to bring some of the mysteries and pleasures of mathematics to a wider public. The adventures of Beremiz Samir, The Man Who Counted, take the reader on a journey in which, time and again, Samir summons his extraordinary mathematical powers to settle disputes, give wise advice, overcome dangerous enemies, and win for himself fame, fortune, and rich rewards. We learn of previous mathematicians and come to admire Samir’s wisdom and patience. In the grace of Tahan’s telling, these stories hold unusual delights for the reader.
A Mathematical Space Odyssey by Claudi Alsina,Roger B. Nelsen Pdf
Solid geometry is the traditional name for what we call today the geometry of three-dimensional Euclidean space. Courses in solid geometry have largely disappeared from American high schools and colleges. The authors are convinced that a mathematical exploration of three-dimensional geometry merits some attention in today’s curriculum. A Mathematical Space Odyssey: Solid Geometry in the 21st Century is devoted to presenting techniques for proving a variety of mathematical results in three-dimensional space, techniques that may improve one’s ability to think visually. Special attention is given to the classical icons of solid geometry (prisms, pyramids, platonic solids, cones, cylinders, and spheres) and many new and classical results: Cavalieri’s principle, Commandino’s theorem, de Gua’s theorem, Prince Rupert’s cube, the Menger sponge, the Schwarz lantern, Euler’s rotation theorem, the Loomis-Whitney inequality, Pythagorean theorems in three dimensions, etc. The authors devote a chapter to each of the following basic techniques for exploring space and proving theorems: enumeration, representation, dissection, plane sections, intersection, iteration, motion, projection, and folding and unfolding. In addition to many figures illustrating theorems and their proofs, a selection of photographs of three-dimensional works of art and architecture are included. Each chapter includes a selection of Challenges for the reader to explore further properties and applications. It concludes with solutions to all the Challenges in the book, references, and a complete index. Readers should be familiar with high school algebra, plane and analytic geometry, and trigonometry. While brief appearances of calculus do occur, no knowledge of calculus is necessary to enjoy this book.
The Mathematical Experience, Study Edition by Philip Davis,Reuben Hersh,Elena Anne Marchisotto Pdf
Winner of the 1983 National Book Award! "...a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." - The New Yorker (1983 National Book Award edition) Mathematics has been a human activity for thousands of years. Yet only a few people from the vast population of users are professional mathematicians, who create, teach, foster, and apply it in a variety of situations. The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it. They also believe that mathematics should be taught to non-mathematics majors in such a way as to instill an appreciation of the power and beauty of mathematics. Many people from around the world have told the authors that they have done precisely that with the first edition and they have encouraged publication of this revised edition complete with exercises for helping students to demonstrate their understanding. This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about. It will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications. The text is ideal for 1) a GE course for Liberal Arts students 2) a Capstone course for perspective teachers 3) a writing course for mathematics teachers. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto ([email protected]) upon request.
Icons of Mathematics: An Exploration of Twenty Key Images by Claudi Alsina ,Roger B. Nelsen Pdf
The authors present twenty icons of mathematics, that is, geometrical shapes such as the right triangle, the Venn diagram, and the yang and yin symbol and explore mathematical results associated with them. As with their previous books (Charming Proofs, When Less is More, Math Made Visual) proofs are visual whenever possible. The results require no more than high-school mathematics to appreciate and many of them will be new even to experienced readers. Besides theorems and proofs, the book contains many illustrations and it gives connections of the icons to the world outside of mathematics. There are also problems at the end of each chapter, with solutions provided in an appendix. The book could be used by students in courses in problem solving, mathematical reasoning, or mathematics for the liberal arts. It could also be read with pleasure by professional mathematicians, as it was by the members of the Dolciani editorial board, who unanimously recommend its publication.
Uncommon Mathematical Excursions: Polynomia and Related Realms by Dan Kalman Pdf
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! This text serves as a tour guide to little known corners of the mathematical landscape, not far from the main byways of algebra, geometry, and calculus. It is for the seasoned mathematical traveller who has visited these subjects many times and, familiar with the main attractions, is ready to venture abroad off the beaten track. For the old hand and new devotee alike, this book will surprise, intrigue, and delight readers with unexpected aspects of old and familiar subjects. In the first part of the book all of the topics are related to polynomials: properties and applications of Horner form, reverse and palindromic polynomials and identities linking roots and coefficients, among others. Topics in the second part are all connected in some way with maxima and minima. In the final part calculus is the focus.
Studying Mathematics by Marco Bramanti,Giancarlo Travaglini Pdf
This book is dedicated to preparing prospective college students for the study of mathematics. It can be used at the end of high school or during the first year of college, for personal study or for introductory courses. It aims to set a meeting between two relatives who rarely speak to each other: the Mathematics of Beauty, which shows up in some popular books and films, and the Mathematics of Toil, which is widely known. Toil can be overcome through an appropriate method of work. Beauty will be found in the achievement of a way of thinking. The first part concerns the mathematical language: the expressions “for all”, “there exists”, “implies”, “is false”, ...; what is a proof by contradiction; how to use indices, sums, induction. The second part tackles specific difficulties: to study a definition, to understand an idea and apply it, to fix a slightly wrong argument, to discuss suggestions, to explain a proof. The third part presents customary techniques and points of view in college mathematics. The reader can choose one of three difficulty levels (A, B, C).
Relax: no one understands technical mathematics without lengthy training but we all have an intuitive grasp of the ideas behind the symbols. To celebrate the 50th anniversary of the founding of the Institute of Mathematics and its Applications (IMA), this book is designed to showcase the beauty of mathematics - including images inspired by mathematical problems - together with its unreasonable effectiveness and applicability, without frying your brain. The book is a collection of 50 original essays contributed by a wide variety of authors. It contains articles by some of the best expositors of the subject (du Sautoy, Singh and Stewart for example) together with entertaining biographical pieces and articles of relevance to our everyday lives (such as Spiegelhalter on risk and Elwes on medical imaging). The topics covered are deliberately diverse and involve concepts from simple numerology to the very cutting edge of mathematics research. Each article is designed to be read in one sitting and to be accessible to a general audience. There is also other content. There are 50 pictorial 'visions of mathematics' which were supplied in response to an open call for contributions from IMA members, Plus readers and the worldwide mathematics community. You'll also find a series of "proofs " of Phythagoras's Theorem - mathematical, literary and comedy - after this, you'll never think of Pythagoras the same way again.